2. One player is not happy with the outcome, and suggests to you, as the officail ranker, that is unfair to give equal importance to first, second and thrid- order influence, and perhaps arbitrary constats could be allocated to weight these influences, that is use:

M+aM2+bM3.... and so forth

If a little money were to change hands, is it possible for you to produce a different ranking, which you can and must justify mathematically?

I have tried many, many, many arbitrary constants.
some of them areM+.75M2+.5625M3....
M+.5M2+.25M3....
M+1/3M2+1/9M3....

Would anybody please be able to exaplin to me if you can make arbitrary canstants that would change to order of the results? i was thinking if the constants are arbitrary then would the order of the athelets stay the same ??

please help cheers(Wink)(Wink)(Wink)

Mar 24th 2013, 04:06 AM

Shakarri

Re: Challenging Matrix Question

Quote:

If a little money were to change hands, is it possible for you to produce a different ranking, which you can and must justify mathematically?

This made me laugh

If you look at the sum of the rows in M, M2, M3, M4; when put in order of highest to lowest they always have the same order so unless the constants are negative which would make no sense.
I only checked up to M4, I didn't prove that in the general case their sums always have the same order but there is certainly a trend.